Please notice that the solution below is just a possible one. Any different solutions
which make sense are also welcomed.
In the stochastic case, the new model is as below:
Maximize
3
123
456
789
1
[1000(
)
750(
)
250(
)]
j
jj
jjj
j
j
P
yyy
=
++
+
+
∑
Suppose Scenario 1 refers to the normal water allocation, Scenario 2 the 10% higher
case and Scenario 3 the 40% lower case. Therefore,
0.5,
0.4,
0.1
PPP
=
==
.
And the constraints for
,1
,
2
,
3
;
1
,
2
9
j
i
yj
i
K
are
And for each i, 0
j
ii
yx
≤≤
.
The constraints for
i
x
are the same as the constraint 1, 3, 4, 5 in the textbook.
Solving this linear programming, we can derive the optimal planting decisions shown
in table below
Allocation (Acres)
Kibbutz
Crop
1
2
3
Sugar beets
100
180
130
Cotton
180
240
80
Sorghum
0
0
0
And the optimal watering decision under Scenario 1 is (80, 106.7, 71.7, 180, 240, 80,
0, 0, 0); under Scenario 2 is (100, 133.3, 84.2, 180, 240, 80, 0, 0, 0); under Scenario 3
is (0, 0, 21.7, 180, 240, 80, 0, 0, 0). The expected return is $63333.3.
Please notice here there is NOT only one optimal solution to this programming.
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 Spring '08
 SteinW.Wallace
 Optimization, optimal planting decisions, stochastic case

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